# How to do basic mathematical computations (in R)

## Task

How do we write the most common mathematical operations in a given piece of software? For example, how do we write multiplication, or exponentiation, or logarithms, in Python vs. R vs. Excel, and so on?

## Solution

For those expressions that need the Python math package, use the code
`import math`

beforehand to ensure that package is loaded. Alternatively,
you can write `from math import *`

and thus drop the `math`

prefixes in
the table below.

Mathematical notation | R code |
---|---|

$x+y$ | `x+y` |

$x-y$ | `x-y` |

$xy$ | `x*y` |

$\frac xy$ | `x/y` |

$x^y$ | `x^y` |

$\vert x\vert$ | `abs(x)` |

$\ln x$ | `log(x)` |

$\log_a b$ | `log(b,a)` |

$e^x$ | `exp(x)` |

$\pi$ | `pi` |

$\sin x$ | `sin(x)` |

$\sin^{-1} x$ | `asin(x)` |

$\sqrt x$ | `sqrt(x)` |

Other trigonometric functions are also available besides just `sin`

,
including `cos`

, `tan`

, etc.

R naturally applies these functions across vectors. For example, you can square all the entries in a vector as in the example below.

1
2

example.vector <- c( -3, 2, 0.5, -1, 10, 9.2, -3.3 )
example.vector ^ 2

1

[1] 9.00 4.00 0.25 1.00 100.00 84.64 10.89

Content last modified on 24 July 2023.

See a problem? Tell us or edit the source.

Contributed by Nathan Carter (ncarter@bentley.edu)